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Hamiltonian Cycle to Hamiltonian Path Reduction (HAMC ≤ HAMP)
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Visualizing the reduction from Hamiltonian Cycle to Hamiltonian Path in 1 minute.
Take a graph G = (V, E) where V are the vertices and E the edges.
For any vertex x in V, it must hold that the HAMC covers that vertex, since it has to cover all the vertices in V.
If we split x up into two new vertices p and q, one for all the outgoing edges of x and one for all the incoming edges, then there must be a HAMP if there was a HAMC before. This way, we map every yes-instance to a yes-instance, and every no-instance to a no-instance.
If anything is unclear or wrong, please let me know in the comments.
Take a graph G = (V, E) where V are the vertices and E the edges.
For any vertex x in V, it must hold that the HAMC covers that vertex, since it has to cover all the vertices in V.
If we split x up into two new vertices p and q, one for all the outgoing edges of x and one for all the incoming edges, then there must be a HAMP if there was a HAMC before. This way, we map every yes-instance to a yes-instance, and every no-instance to a no-instance.
If anything is unclear or wrong, please let me know in the comments.
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